Question

Fifth term of a $GP$ is $2$ , then the product of its $9$ terms is:

• A. 256
• B. 512
• C. 1024
• D. none of these

Answer 1

Answer: (B)

$a{r}^4=2$ ... (i)
Let $a$ be the first term and $r$ be the common ratio, then according to the given condition.
Since, $a\times ar\times a{r}^2\times a{r}^3\times a{r}^4\times a{r}^5$
$\times a{r}^6\times a{r}^7\times a{r}^8$
$=a^9{r}^{36}=(a{r}^4{)}^9=2^9=512$